Abstract This paper is devoted to the study of long-time dynamics of a Cauchy problem related to extensible beam models with dissipative effects coming from the nonlocal Balakrishnan-Taylor and the localized weak damping terms in R n . Our first main result features a new unique continuation property for models associated with extensible beams. Then, applying such a property and with the fundamental aid of the nonlocal Balakrishnan-Taylor damping term, we state and prove our second main result dealing with the existence, characterization and regularity of a compact global attractor for the corresponding nonlinear dynamical system.

中文翻译：

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在非局部和局部阻尼效应下与可扩展梁相关的柯西问题的动力学

摘要 本文致力于研究与可扩展梁模型相关的柯西问题的长期动力学，其耗散效应来自非局部 Balakrishnan-Taylor 和 R n 中的局部弱阻尼项。我们的第一个主要结果为与可扩展梁相关的模型提供了一个新的独特的连续属性。然后，应用这种性质并借助非局部 Balakrishnan-Taylor 阻尼项，我们陈述并证明了我们的第二个主要结果，该结果涉及相应非线性动力系统的紧凑全局吸引子的存在、表征和规律性。